Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  cmbri Structured version   Unicode version

Theorem cmbri 23084
 Description: Binary relation expressing the commutes relation. Definition of commutes in [Kalmbach] p. 20. (Contributed by NM, 6-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
pjoml2.1
pjoml2.2
Assertion
Ref Expression
cmbri

Proof of Theorem cmbri
StepHypRef Expression
1 pjoml2.1 . 2
2 pjoml2.2 . 2
3 cmbr 23078 . 2
41, 2, 3mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725   cin 3311   class class class wbr 4204  cfv 5446  (class class class)co 6073  cch 22424  cort 22425   chj 22428   ccm 22431 This theorem is referenced by:  cmcmlem  23085  cmcm2i  23087  cmbr2i  23090  cmbr3i  23094  pjclem1  23690  pjci  23695 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-iota 5410  df-fv 5454  df-ov 6076  df-cm 23077
 Copyright terms: Public domain W3C validator